Head of airline's very happy to drop off old fighter pilot (7)

I believe the answer is:

aviator

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'pilot' is the definition.
(I've seen this before)

I don't understand how the remainder of the clue works.

(Other definitions for aviator that I've seen before include "Aircraft pilot" , "One flying aircraft" , "He travels up" , "Air pilot" , "Woman in a flying machine" .)

I've seen this clue in The Independent.

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